The utility of congruence lattices in revealing the structure of
general algebras has been recognized since Garrett Birkhoff's pioneering work
in the 1930s and 1940s. However, the results presented in this book are of very
recent origin: most of them were developed in 1983. The main discovery
presented here is that the lattice of congruences of a finite algebra is deeply
connected to the structure of that algebra. The theory reveals a sharp
division of locally finite varieties of algebras into six interesting new
families, each of which is characterized by the behavior of congruences in the
algebras. The authors use the theory to derive many new results that will be
of interest not only to universal algebraists, but to other algebraists as
well.

The authors begin with a straightforward and complete development of basic
tame congruence theory, a topic that offers great promise for a wide variety of
investigations. They then move beyond the consideration of individual algebras
to a study of locally finite varieties. A list of open problems closes the
work.